This award supports a multidisciplinary team of four investigators using modeling, analysis, computer simulations, and experiments to study using suspensions of active particles to enhance the properties of inks for applications in 3D printing. Active materials represented by suspensions of synthetic self-propelled particles harvest energy from their environment and alter the properties of the surrounding fluid. They have novel materials properties and promising applications. Here, a new concept of ink for 3D printing, termed "active ink", is introduced. Even a small fraction of active self-propelled particles in a fluid results in a dramatic reduction of viscosity, enhancing ink transport through the nozzle and increasing printing speed. This project will facilitate the design and manufacture of new materials, significantly shortening the path from prototype to product. This research will also enable a highly multidisciplinary training and education of students and postdocs who will learn theoretical techniques in applied mathematics and computations, as well as experimental techniques employed in chemistry and nanofabrication. Apart from the development of new 3D printing technology, the work will lead to novel mathematical models and efficient computational algorithms.
A drastic reduction of effective viscosity and increase of self-diffusivity of the active ink due to the presence of synthetic self-propelled particles will be studied. The reduction of the effective viscosity will enhance ink transport through the nozzle. The increase of the effective self-diffusivity will enable faster polymerization resulting in resolution enhancement and more accurate 3D feature design. In addition, due to their fundamentally different response to applied shear flow, the use of active particles may lead to the design of composite materials with novel distributions of particles. The functionalization of active particles also will allow tuning the properties of the hardened polymer. New mathematical models will be developed and analyzed both numerically and analytically. Their predictions will be experimentally verified. The continuum partial differential equation model based on kinetic theory will be analyzed asymptotically and numerically. A key challenge here is to find stationary flow solutions by employing methods from fixed-point and topological degree theory. In simulations of particle-based models, the challenge is to accurately capture the dynamics of the reaction that occurs as the active rods move. A difficulty in simulations of the continuum model is incorporating the molecular-scale reactions into a mesoscale approach. By addressing these challenges, the utility and applicability of these computational methods will be significantly expanded, allowing them to be used for simulating a broad range of multi-component, dynamical systems.
